Examine the function f(x)=∣x3−3x∣ on the closed interval [−2,2].
a. (i) Determine all critical points of f inside (−2,2), including those where the derivative does not exist.
b. (ii) Using an appropriate test, classify each critical point obtained in part (i) as a point of local maximum, local minimum or neither.
c. (iii) Evaluate f at the critical points and at the endpoints to identify the absolute maximum and absolute minimum of f on [−2,2].